Ideal magnetohydrodynamic equations for low-frequency waves in toroidal plasmas

Fesenyuk, O. P.; Kolesnichenko, Ya. I.; Wobig, H.; Yakovenko, Yu. V.

doi:10.1063/1.1462633

Cited by 22 publications

(25 citation statements)

References 21 publications

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“…26: ͉K͉ = O͑⑀ / a͒, where K = ͑b · ٌ͒b is the magnetic field curvature, ٌ͉B 0 ͉ = O͑⑀B 0 / a͒, and ٌ͉ ʈ B 0 ͉ = O͑⑀ 2 B 0 / a͒. It suggests that interaction with the other Alfvén modes should be weak, which is corroborated by the numerical results ͑e.g., Refs.…”

Section: Appendix A: Reduced Mhd Equationssupporting

confidence: 58%

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Beta-induced Alfvén-acoustic eigenmodes in stellarator plasmas with low shear

Eremin¹,

Könies²

2010

Physics of Plasmas

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The coupling of low-frequency Alfvénic modes with acoustic oscillations due to curvature of the background magnetic field is considered for stellarator plasmas with low shear. Magnetohydrodynamic ͑MHD͒ analysis demonstrates that the interaction between these branches can generate gaps in the continua with a width proportional to beta as well as the magnitude of the Fourier harmonics of the magnetic field strength which cause the coupling. The gaps can provide a habitat for beta-induced Alfvén-acoustic eigenmodes ͑BAAEs͒. Using the causality principle, a technique is developed to resolve the singular behavior of the MHD BAAE eigenmode equation at the points of resonance with the acoustic continuum. Alternatively, the singularities arising in the reduced MHD description can be resolved by accounting for the finite parallel electrical field. Both approaches yield consistent continuum damping rate, which proves to be small. Numerical calculations for analytically fitted experimental profiles of electron-dominated plasma in Helically Symmetric eXperiment ͑HSX͒ facility yield two weakly damped BAAE modes with different frequencies: one is close to the maximum of the lower-frequency Alfvén-acoustic continuum, and the other is located well within the BAAE gap. The numerically found BAAEs have frequencies in the same range as the experimentally observed electromagnetic modes in HSX, even when the finite diamagnetic frequency effects are considered.

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Section: Appendix A: Reduced Mhd Equationssupporting

confidence: 58%

“…26 and using a representation of the perturbed magnetic field in terms of the vector potential, from To derive the second equation, which will govern the shear Alfvén mode, one employs the quasineutrality equation in the form ٌ · j= 0.…”

Section: ͑A8͒mentioning

confidence: 99%

Beta-induced Alfvén-acoustic eigenmodes in stellarator plasmas with low shear

Eremin¹,

Könies²

2010

Physics of Plasmas

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“…[11,13]), where K is the field line curvature, we express ζ 10 in terms of Φ ′ 00 and find that the contribution of .27) and using the resonance condition ∥ ω = v qR s , we arrive at equations (17) and (18). Similarly, equations (40) and (41) …”

Section: The Circle Approximates the Fast-ion Birth Velocity (ˆ∥mentioning

confidence: 99%

“…Because experimentally measured magnitude is the amplitude of the electron density fluctuation, n, let us express Ê r through n. This can be done by proceeding from ideal MHD equations (e.g. those derived in [13]), which couple the electric potential and plasma compressibility through the field line curvature. As a result, we obtain (see [11]):…”

Section: Motion and Change Of The Energy Of Resonant Ions In The Gam mentioning

confidence: 99%

Manifestations of the geodesic acoustic mode driven by energetic ions in tokamaks

Kolesnichenko

Lutsenko

Yakovenko

et al. 2016

Plasma Phys. Control. Fusion

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Effects of the energetic-ion-driven Geodesic Acoustic modes (GAM and E-GAM) on the toroidally passing energetic ions and the concomitant change of the neutron yield of beam-plasma fusion reactions in tokamaks are considered. It is shown that due to large perturbations of the plasma density, the resonant energetic ions driving the instability can be considerably slowed down for a few tens of the particle transit periods, which is much less than the collisional slowing down time. The time of the collisionless slowing down is actually determined by the period of the particle motion within the resonance island arising because of the GAM / E-GAM. Being trapped in the island, the resonant particles can not only lose their energy but also gain it. One more effect of GAMs is the flattening on the distribution function of the resonant particles. Due to conservation of the canonical angular momentum during a GAM / E-GAM instability, the change of the particle energy is accompanied by a radial displacement of the resonant particle for a distance up to the poloidal Larmor radius of energetic ions. The particles are displaced inwards or outwards, depending on the direction of their motion along the magnetic field. Expressions describing the change of the neutron yield due to GAM modes are derived. It is found that the distortion of the velocity distribution of the resonant particles can lead to a considerable drop of the neutron emission even when effects of the particle radial displacement are small. The developed theory is applied to an E-GAM experiment on the DIII-D tokamak. Relations for the period of the motion within the resonance island of passing (both well passing and marginally passing) particles and the width of the resonance of the energetic particles with GAM modes and low-frequency Alfvén modes are derived.

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“…Model. Introducing the current due to finite Larmor radius effects [6] into the Alfvén wave equation [7], we obtain…”

mentioning

confidence: 99%

Theory of generation of kinetic Alfvén waves by Non-conventional Global Alfvén Eigenmodes

Fesenyuk¹,

Yakovenko²,

Kolesnichenko³

et al. 2010

Nucl. Fusion

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The process of radiation of kinetic Alfvén Waves (KAWs) by a non-conventional global Alfvén eigenmode (NGAE) or a reversed-shear Alfvén eigenmode (modes which exist above maxima of Alfvén continuum branches) is studied analytically and numerically. The Schrödinger equation describing a localized NGAE and emitted KAWs in the space of radial wave number is derived. Analytical expressions for the mode eigenfrequencies, the radiative damping rates and the wave amplitudes are obtained. The results obtained analytically are in agreement with those obtained numerically by means of two codes based on different methods. It is found that the amplitude of the radiated KAWs can be as large as the amplitude of the radiating mode, with the radiative damping rate being rather small.

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Ideal magnetohydrodynamic equations for low-frequency waves in toroidal plasmas

Cited by 22 publications

References 21 publications

Beta-induced Alfvén-acoustic eigenmodes in stellarator plasmas with low shear

Beta-induced Alfvén-acoustic eigenmodes in stellarator plasmas with low shear

Manifestations of the geodesic acoustic mode driven by energetic ions in tokamaks

Theory of generation of kinetic Alfvén waves by Non-conventional Global Alfvén Eigenmodes

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